Barrett's (1994) paper on transboundary pollution abatement shows that if the signatories of an international environmental agreement act in a Stackelberg fashion, then, depending on parameter values, a self-enforcing IEA can have any number of signatories between two and the grand coalition. Barrett obtains this result using numerical simulations in a pollution abatement model where he is not constraining emissions to be non-negative. Recent attempts to use analytical approaches and to explicitly recognize the non-negativity constraints have suggested that the number of signatories of a stable IEA may be very small. The way such papers have dealt with non-negativity constraints is to restrict parameter values to ensure interior solutions for emissions. We argue that a more appropriate approach is to use Kuhn-Tucker conditions to derive the equilibrium of the emissions game. When this is done we show, analytically, that the key results from Barrett's paper are maintained. Finally, we explain why his main conclusion is correct although his analysis can implicitly imply negative emissions. Copyright 2006, Oxford University Press.